Neela's clock is broken the minute hand rotates around the clock correctly but the hour hand is stuck in the three o'clock position. Suppose neela first looks at the clock when the hands are aligned and it shows 3:15. She looks at the clock again and sees that the hour and minute hands of the clock form the arms of an angle measuring -105 degrees. How many degrees could the minute hand have rotated to reach its current position?

Question

a. -465 degrees
b. -375 degrees
c. -435 degrees
d. -95 degrees

I am so confused. Please help!!!

Answer 1

3:30 is -90, 3:45 is -180

Answer 2

-465

Answer 3

A clock goes 360° in 12 hours, so 360/12 = 30° and that means every hour is 30°. 15/60 = 0.25 and 0.25 * 30° is 7.5, so 3:15 is -7.5° (note it is in Quadrant IV, where angles are negative in terminal position). None of the answers, however, include a ".5" to get it to 105, which is a whole number. But... if "when the hands are aligned" means that both hands are in the exact same spot, then it's "0°," if you will, is actually at 7.5°.
So! 105 + 7.5 = 112.5, and that's the final position's actual degree if the starting point was terminal position, which it is not.
Now, the least amount of degrees is actually just -105 itself. But that's not an option, so what gives you the same placement? Adding 360.
360 + 105 = 465, and boom, there's your answer. -465.
Seriously this problem gives me a headache, it took me way too long to figure this out. Just thought I'd put the explanation here for anyone skeptical of biscuits' answer, which I was myself.

Answer 4

Whoops, forgot a few negative signs here and there, but you guys get the point.
*it's "0°," if you will, is actually at -7.5°.
*-112.5, and that's the final position's actual degree if the starting point was terminal position
And let me just fix this so it's clearer...
*Now, the least amount of degrees you can add to get it to -105 is...